Fig 1.
Extensive-form game tree: Sir Philip Sidney game.
Table 1.
Matrix of inclusive fitness given p = 1.
B is the row player and D is the column player.
Table 2.
Matrix of inclusive fitness given p = 0.
B is the row player and D is the column player.
Table 3.
Alternative categorisation of example parameter values that satisfy each set of inequalities.
For expectation, means the Beneficiary does not signal, and the Donor keeps the resource. Valid for any value of p.
Fig 2.
Visual representation of threshold values where the evolutionarily stable strategies presented in this article would hold ().
The intersection of r = 0.8 with both c = 0.25 and c = 0.75 is within the shaded area of the two inequalities, therefore both thresholds are satisfied and we would expect the resulting strategy combination to be . However, for r = 0.2, the evolutionarily stable strategies of Not signal and Keep only hold for low signal costs as the intersection with c = 0.75 is outside the shaded area.
Table 4.
Resulting strategies of learning agents, showing the top strategy learned and the proportion of runs this was the resulting strategy for the parameters LR=0.9, DR=0.1.
For expectation, means the Beneficiary does not signal, and the Donor keeps the resource. Valid for any value of p.
Fig 3.
Beneficiary resulting strategies.
Percentage of runs that the Beneficiary learns each strategy. Not thirsty state, . Strategies described in Table 5.
Fig 4.
Percentage of runs that the Donor learns each strategy. Not thirsty state, . Strategies described in Table 6.
Table 5.
Strategies most often learned by the Beneficiary with parameters S = 0.2, V = 0.2, r = 0.5 (Case 1), see Fig 3.
Table 6.
Strategies most often learned by the Donor with parameters S = 0.2, V = 0.2, r = 0.5 (Case 1), see Fig 4.
Fig 5.
Q-values Case 2, darker line is average across all, faint lines are average for each state.
Fig 6.
Q-values Case 3, darker line is average across all, faint lines are average for each state.